Spatial Population Models for Animals - Environmental Modelling: Finding Simplicity in Complexity - page 213

difficulties of manipulating and observing whole ecosys-
tems, and hence the need to up-scale, are quite obvious,
although similar logistical difficulties may also apply to
nonmanipulative studies (Eberhardt and Thomas, 1991).
Questions of how to move information across scales is an
area of active research, and the pitfalls that beset inappro-
priately scaled research are well known (Mac Nally, 2002;
Miller et al ., 2004). Some have gone so far as to argue
that scaling difficulties makes the experimental approach
of little relevance to community and ecosystem ecology
(e.g. Carpenter, 1996). Yet, while an holistic ecosystem-
level focus makes an attractive goal for experiments, the
sheer logistics and expense of conducting even single
trials (ignoring issues such as replication and the avail-
ability of logical controls) will often prove too difficult
(Turner et al ., 1995). In addition, the decision tomanipu-
late at the ecosystem level typically comes only once ideas
about important processes at work within the systemhave
become reasonably well established, typically via smaller
scale experiments.
The point of the foregoing discussion is to highlight the
difficulties that complexity and scale impose on our abil-
ity to understand the dynamics of ecosystems using direct
methods of observation and experimentation, particu-
larly across large spatio-temporal extents. As we discuss
in this chapter, quantitative modelling is increasingly
being used to answer questions at these large spatial
scales because of the relative ease with which logisti-
cal problems can be overcome (Hastings et al ., 2005a).
Modelling has become a valuable strategy for increasing
ecological understanding at both small and large spa-
tial scales, and now plays a key role in the progression
and consolidation of knowledge in ecology, from cases
where we are relatively knowledge and data poor (in
which exploratory models help guide development), to
cases where our knowledge and data are rich, permitting
the creation of complex predictive models (Perry and
Millington, 2008). Although we touch on data-driven
models of species distributions, in keeping with the title
of this topic, our focus is on the role that exploratory
models can play in tackling any particular ecological
problem. We begin by examining the historical devel-
opment of ecological modelling, as well as more recent
approaches (focusing on spatially explicit models, both
static and dynamic) drawing examples from the 'animal
ecology' literature. Nevertheless, many of our general
points are relevant to all types of spatial (ecological)
modelling.

13.2 Finding the simplicity: thoughts
on modelling spatial ecological
systems

13.2.1 Space, spatial heterogeneityandecology

Mathematical modelling has a long and rich history in
ecology (Kingsland, 1995). Models such as the logis-
tic (Verhulst) and the Lotka-Volterra have been cen-
tral to the development of ecological theory. Typically,
these 'classical' ecological models have been concerned
with stable equilibria and have assumed that ecologi-
cal interactions take place in a spatially homogeneous
environment in which every individual is equally acces-
sible to every other individual (the so-called 'mean-field'
assumption - Hastings, 1994). The reasons behind the
adoption of this view are many but are largely centred on
a desire to keep theoretical and experimental studies rela-
tively simple (Wiens, 1997). The resultingmodel takes the
form of a series of difference or differential equations for
the mean abundance of the various model elements (e.g.
individuals in a population, the abundance of different
species). Although several seminal early papers (notably
Watt, 1947; Skellam, 1951; Huffaker, 1958) addressed the
role of space in ecological dynamics, it has only been in
the last 30 years that ecologists have come to see space
as something more than a statistical nuisance. As spatial
heterogeneity has become explicitly considered in ecolog-
ical field studies, experiments and models, it has become
obvious that spatial patterns and process are of fun-
damental importance in many situations. For example,
local species richness may be related to habitat hetero-
geneity (Tilman, 1994), populations and predator-prey
interactions may be more stable or persistent in patchy
environments (Kareiva, 1990), the spread of contagious
disturbances such as fire or pathogen outbreaks is altered
by, and also generates, patchiness (Peterson, 2002), and
dispersal and recruitment are influenced by the patch
structure of the environment (Bond and Perry, 2000).

13.2.2 Staticapproaches

Static models of animal populations are concerned
with spatial distributions in the past, present and
future. The development of new tools for predicting
species distributions has become an area of growing
concern as the need to evaluate the extent to which
species can 'keep up' with pressures such as changing